Study 29 Continuous Model Shear

Study 29 — The continuous-model shear

File name note. This page is served as Study-29-Affine-Earth-Sovereign-Substrate.md. The name is kept so inbound cross-links survive; the subject of the page is the reentry-mass ledger and the continuous models that consume it.

Status word, and the half of the index's rule that does not fit. The program index defines OPEN as the stage at which "we do not yet have ingested data / frozen integers", and adds that a named archive is not OPEN if a stronger term already applies. Only one half of that definition fits this page, and the departure is stated rather than glossed. The forcing corpus is ingested, digest-pinned and censused, and this page's gate integers are frozen — by the index's own wording that is past OPEN, and Study 10 holds CHARTER WITH ARCHIVE on less. The response corpus is not ingested, no granule has been pulled and no gate has been run, which is the Study 26 / Study 27 condition. The board word stays OPEN as the weaker of the two, and the split is: forcing half at corpus stage with frozen integers, response half at charter stage.

What has run and what has not. A descriptive corpus census of the forcing ledger has been run and is published below over all nineteen band slots, all twelve months of 2025, all eight complete months of 2026 and four annual populations. A flip census has not been run. A confinement census has not been run. No response granule has been pulled. Every number on this page is either a measurement of the forcing catalogue, an exact rational re-derived from a published paper's own printed figures, or a threshold frozen here before scoring. This page charters a test and delivers no verdict about any atmosphere.

Every decimal this page computes is a display of an exact rational, and no decimal enters any comparison, gate or seal. Third-party measured values with their own stated uncertainty — 0.4 ± 0.2 Tg, 0.015 ± 0.007, 1.1 µm, 3.0 × 10¹⁹ m⁻³ — are carried as their sources print them and are never converted into a graded quantity. Every grading statistic below is an integer cross-multiplication.

Provenance markers. Third-party figures carry VERIFIED (primary source fetched and read this pass), REPORTED (a real published figure whose primary text did not fetch this pass), UNKNOWN (named as not retrieved), or UNVERIFIED_FROM_PRINT (quoted from a source whose page pointer could not be located this pass).

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The shear, in one paragraph

A satellite reentering the atmosphere is a discrete, countable, exactly-ledgerable event: N objects of known dry mass, reentering at known epochs, on orbits of known inclination. The field models what that material does after it arrives with continuous, floating-point chemistry-transport models, and those models disagree on the sign of the ozone response. Ferreira, Huang, Nomura and Wang (Geophysical Research Letters 51, e2024GL109280, 2024, doi:10.1029/2024GL109280 — REPORTED, publisher returned HTTP 403 to every method tried this pass) report a chlorine-activation mechanism and quantify mass only, reporting no ozone percentage. Maloney, Portmann, Ross and Rosenlof (Journal of Geophysical Research: Atmospheres 130(6), e2024JD042442, 2025, doi:10.1029/2024JD042442 — REPORTED) run WACCM6 coupled to the CARMA sectional model at a 10 Gg/yr Al₂O₃ flux and report ~1.5 K temperature anomalies, a ~10% reduction in Southern Hemisphere polar-vortex wind speed, and a weaker springtime ozone hole — the opposite sign. Revell, Bannister, Brown and colleagues (npj Climate and Atmospheric Science 8:212, 2025, doi:10.1038/s41612-025-01098-6 — REPORTED) run SOCOLv4 with prognostic alumina microphysics and find at most a +0.27% ozone increase at 10 hPa in the Northern Hemisphere, arising from acceleration of the shallow Brewer-Dobson branch under alumina heating; their alumina is launch alumina and the paper does not simulate reentry emissions, offering the result explicitly as a comparison point for satellite reentry ablation. Barker, Marais and colleagues (Earth's Future, 2026, doi:10.1029/2025EF007229 — REPORTED, volume and article number not verified) find ozone loss dominated by chlorine from solid propellant with megaconstellation missions at 9%, and report rocket black carbon flipping sign between +6.47 mW/m² instantaneous and −6.40 mW/m² stratospherically adjusted forcing — one model, one emissions set, two forcing definitions, zero difference in input data. Vliex and colleagues (Earth's Future, 2026, doi:10.1029/2025EF007795 — REPORTED) run GEOS-Chem and report 87.7% of the modelled ozone depletion driven by NOx from reentry, 85.6 mDU annual global column loss, net forcing 4.1 mW/m², with plume chemistry reducing ozone depletion by 17.1% and forcing by 29.1% — a third position on the same dominant-species axis. Published models disagree on the sign of the ozone response and on the species to which they attribute it, and that disagreement is the shear signal under test. Whether that spread is attributable to declared admission rules and declared conversion coefficients rather than to any observation is exactly what this court's Act 1 scores, and LOSS (i) is frozen below for the case where it is not. This court is chartered to re-execute the counting half in exact integers — grams and centi-degrees, from one anonymous file — so that whether the arithmetic spread and the physical spread can be told apart becomes a scored question rather than an assumed one. The claim class, verbatim and load-bearing: a presented configuration is verified; an unknown configuration is not searched.

The forty-ninth instance

This study is the forty-ninth instance of a pattern the substrate already serves publicly forty-eight times.

Measured live on 2026-09-01 at https://affine.earth/language-invariant/games — HTTP 200, anonymous, no token: 48 domains, 88 roles, 54 capabilities, 13 games, no_float: true on 48 of 48, flourishing_kind GUIDE_PUBLIC_FLOURISHING_ALL, pricing_axis entropy_delta_dh_structural. Re-derived from the same response: 122 distinct may_ingest field names, and a dead_equation / new_law pair present on 48 of 48.

Every domain carries the same skeleton:

domain	dead_equation — the continuous form	new_law — the exact integer form
geometry	vol = integral_P 1 dx	h_P(t)=|tP intersect Z^d|; vol = Delta^d h(0)/d!
chance	Pr = |alpha|^2 in R	W_n = (3/4)^n in Q
cs	IEEE-754 sums; float loss + backprop	a/b + c/d = (ad+bc)/bd; SHA256d lock
finance	Black-Scholes PDE; GBM + VaR Monte Carlo	tick in Z; PnL = lots * ticks; discount n/d per period
fluids	Navier-Stokes + RANS closures; Re = UL/nu	sum Phi = 0 exact; L(gamma)=(q,r); vol = Delta^d h(0)/d!
qcd	alpha_s(Q^2) running in R	same h_P; UV = small t; IR = large t; no isolated color row
health	C = C0 e^{-k t}; p-value; Cox e^{beta X}	C = n_mass / d_vol exact rational; WIN/MISS on assay counts

A continuous-model shear study is an instance of that catalogued, publicly-served discipline, and any reader can check the count with one anonymous GET.

And a passing gate is a pass, not a proof of absence — the page that grades other people's instruments states this about its own. The no_float field is a served declaration, and the substrate's own float ratchet, which prints current: 0, is a pattern match: measured this pass, 24 float-typed declarations live inside the paths that ratchet scopes — 19 in one module, 5 in another — written as [Double], <Double>, Float32 or a bare colon-Float, none of which its pattern matches, and one of its scoped paths does not exist, so its absence reads to the ratchet as a zero. The gates on this substrate are cited here as passing and never as proof that no float exists. That is the same standard this page applies to a published model's declared coefficients, and it is applied first to the instrument the page is written on.

Section zero — the discrimination gate

Before any row is scored, each detector must be shown able to fail. A gate that cannot fail is not a gate; always-green and always-red are the same defect. Everything in this section is frozen in this charter before any admission rule is executed and before any response granule is requested. The descriptive corpus census reported in the frozen-integers section has already run; the flip census and the confinement census have not.

The four losses, each graded as a loss and published as one

• LOSS (i) — the flip set is empty. Every declared admission rule carrying a complete frozen operator chain, re-executed on the identical frozen rows, ranks every calendar month and every latitude band identically. Then the field's ledger spread is not attributable to declared admission rules, the exact ledger buys nothing here, and the study publishes the census totals with the zero on the page.
• LOSS (ii) — the confinement census fires everywhere. Scored form, frozen, with both denominators named: let a_lo be the summed anomaly count over the two low-load bands (b=9 and b=15) and a_hi the summed count over the three leading bands (b=8, b=10, b=16). The criterion is that the per-band mean in the low-load arms reaches one quarter of the per-band mean in the leading bands — cross-multiplied into integers, LOSS (ii) prints when 6 × a_lo ≥ a_hi. The ratio 1/4, the band memberships and the two denominators are frozen here and do not move.
• LOSS (iii) — the sealed adversary is not separable on shape. Scored form, frozen: the confinement concordance computed against a sealed adversary's own month vector must fall below the frozen threshold n/d while the ledger's own concordance exceeds it. If a sealed adversary's month vector clears the same threshold the ledger clears, the two are not separated on shape at this instrument's resolution and LOSS (iii) prints. Separating on size is forbidden by the program recipe, so no magnitude comparison may rescue it.
• LOSS (iv) — a declared rule is not reproducible from its own print. A rule whose published chain does not close against its own published figures prints UNREPRODUCIBLE_FROM_PRINT, is excluded from the flip census at the step that does not close, and is published in its own row. LOSS (iv) has already fired once, on Ferreira et al. 2024's population chain; the consequence is stated in full in the admission-rule section below.

Fourteen control arms — eleven tabled, three stated after the table

Arm	Fires on	Non-discriminating twin, published as a labelled smoke test
A — admission-rule flip	Barker's declared rule set with exactly one exact rational replaced: the indirect thermal-NOx index moved from Barker's frozen 2/5 to Ryan's 1, which is the direction the field's own verbatim statement documents. The census must seal a non-zero flip set against the unmutated rule. The index is class-dependent — Barker carries 7/40 for reusables against 2/5 for discarded — and the graded statistic mixes species, so the replacement is not a uniform positive rescale and can move a rank order.	Total annual event count. Identical across rules that differ only on mass coefficients. Count does not discriminate mass rules.
B — population absence	The 654 rows whose DryMass reads 0 must each print MASS_ABSENT and must never contribute 0 g to any sum. A query for a status class the year does not carry prints POPULATION_ABSENT, never 0 t. The probe class is pinned at corpus stage by enumerating every Status value in the 2025 slice and taking the first with count 0; that value is owed and is named as owed.	—
B2 — granule absence	A request to OMPS_NPP_LP_L2_AER_DAILY v2.5 on a date for which CMR returns zero granules must print GRANULE_ABSENT, never a null anomaly. The product and version are frozen here; the specific date is pinned at corpus stage from a CMR temporal query over the documented sparse window (roughly one day per week, 2012-04 to 2016-06) and is owed.	—
C — estimate	The 864 rows / 349,108,250 g carrying the catalogue's own ? estimate flag print MASS_ESTIMATED and are censused separately, with both denominators published — flagged 864 rows / 349,108,250 g and unflagged 1,043 rows / 112,105,259 g.	—
D — epoch precision	Rows print one of six declared classes, read from the date string's own token count and trailing marker: EPOCH_MINUTE, EPOCH_MINUTE_UNCERTAIN, EPOCH_DAY, EPOCH_DAY_UNCERTAIN, EPOCH_YEAR_ONLY, and EPOCH_UNCLASSED for a token pattern in none of the five — the catalogue carries quarter-precision values (2023 Q4?) that land there. Measured 2025: 501 / 219 / 1,162 / 23 / 2 / 0. The sixth class is not decorative: it is non-empty in three of the four annual populations censused below (2 in 2022, 2 in 2023, 21 in 2024), so a five-class set would be exhaustive over the 2025 slice alone while Piece 4 registers forward months under the same arm.	—
E — gram exactness	A DryMass value carrying four decimal places, injected into a copy of the corpus, must be rejected with MASS_NOT_GRAM_EXACT. Measured on the real corpus: 1,907 of 1,907 pass, 0 fail — a gate always green on real data tells you nothing until you make it fire, so the census program carries the injection as a printed control arm: 1.234 admits at 1,234 g, 1.2345 and 12x and the empty string all print MASS_NOT_GRAM_EXACT.	—
F — confinement shuffle null	Permute the ledger's inclination column within the year under the frozen integer seeds 20260831 … 20260850 (twenty permutations). Collapse threshold, frozen: at least 19 of the 20 permutations must fail the same n/d criterion the unshuffled ledger is scored against. A score that survives the shuffle is reading the archive's own latitudinal structure, not the ledger's.	—
F2 — low-load bands	Bands [45°, 50°) (10 rows, 2,614,000 g, 0.57% of 2025 mass) and [75°, 80°) (11 rows, 1,000,000 g, 0.22%) sit between the leading bands. The frozen comparison is LOSS (ii)'s: 6 × a_lo ≥ a_hi prints the loss.	—
F3 — zero-gram null band	Slot b=18, the boundary bin at tc = 9000 centi-degrees (inclination exactly 90.00°), carries 0 rows and 0 g across the whole 2025 population — 18 of 19 slots populated, measured. It is the arm on which any mass-proportional response must return no anomaly, and it is a true zero, not a small number.	—
G — adversary, hydration	The exclusion arm must fire on 2022-01 — Aura MLS ML2H2O must show the January-2022 stratospheric water anomaly. If it does not, the arm is broken and no physics is scored. The pressure level and the integer threshold are derived at corpus stage from the ML2H2O record and frozen before the first pre-registered month; both are owed.	—
H — composition	Al/Fe > 1/10, an exact rational, on single-particle spectra. Scope carried at the point of use: the quoted figure is a Figure 5 caption over the SABRE 2023 Alaska flights, n ≈ 175,000 particles, on a closed five-week campaign archive with no forward cadence, so this arm is not part of the forward-registered separation.	Mg/Fe. Murphy, Abou-Ghanem, Cziczo, Froyd, Jacquot, Lawler, Maloney, Plane, Ross, Schill and Shen (PNAS 120(43), e2313374120, 2023, doi:10.1073/pnas.2313374120 — VERIFIED), Figure 5 caption, verbatim: "The Mg/Fe distribution is much tighter than the Al/Fe distribution because meteors dominate the source of Mg and Fe." It returns the same answer under both hypotheses.

Arm G2 — adversary, ascending front. The front-direction arm must fire on austral summer 2019/20, a documented self-lofting stratospheric smoke event. A detector that cannot identify an ascending front cannot certify a descending one. The level, the integer threshold, the unit and the window for this arm are not frozen on this page and are owed at corpus stage, alongside arm G's.

Arm I — the agreement control. A low-forcing month is not an agreement control: declared admission rules differ on which rows they admit, so two rules can legitimately render different band vectors on a 13-event month. The control is therefore built the way Study 28 built its winter control — on a property that forces agreement. Frozen construction, in two steps, because the second does not hold without the first: (1) the row set is drawn from a single object class that every rule entering the flip census admits, and that admission is verified per rule before the control is scored; a class any entering rule excludes renders an empty vector and disqualifies the set. (2) On a set every entering rule admits, each rule's operator is a single positive rational applied to every row, a positive scalar multiple preserves every rank order, and every entering rule must render an identical band rank vector. A disagreement there is a broken scorer, not a finding, and the study halts. The specific class — one bus, one Type prefix, DryFlag unflagged, Inc present, with the per-rule admission check recorded — is pinned at corpus stage and is owed.

Three low-forcing months are published as low-forcing arms, and each is reproducible from the pinned corpus by the census program named in the reproduce section, run at that year: 2016-08 (13 events, 324,000 g), 2016-02 (19 events, 64,500 g), 2020-06 (11 events, 66,000 g). Every calendar month searched this pass carries a non-zero forcing count; no month-by-month census of the whole record is published here, so these are the three lowest found this pass and not the minimum of the record.

Arm J — the cross-catalogue arm, with its denominator declared. The catalogue's 2025 reentry population against ESA's independently compiled Annual Space Environment Report (GEN-DB-LOG-00288-OPS-SD, Issue 10.0, 1 May 2026 — REPORTED): 1,904 events / 456,038,509 g on Status ∈ {R, AR} against ESA's 1,881 / 486.7 t. The declared denominator is this study's own catalogue, and both readings are printed so a reader can check either:

Spread	Difference	On the catalogue's denominator	On ESA's denominator
events	23	23 / 1,904 = 1.21%	23 / 1,881 = 1.22%
payloads	7	7 / 1,124 = 0.62%	7 / 1,117 = 0.63%
mass	30,661,491 g	30,661,491 / 456,038,509 = 6.72%	30,661,491 / 486,700,000 = 6.30%

Population note, stated because it decides the payload row: the 1,124 payload count is drawn from the {R, AR, D} population of 1,907, while the event and mass rows are on {R, AR} = 1,904. The {R, AR} payload count is not separately measured on this page; since Status D is exactly 3 rows, it lies in [1,121, 1,124] and the payload spread is bounded by that interval. The {R, AR} payload census is owed. ESA's 1,117 payload figure is read from a table denominator in that report and not from a stated payload count, and it carries the REPORTED marker for that reason. Frozen tolerance band, as exact rationals on the catalogue's denominator, cross-multiplied in integers: events ≤ 1/20, payloads ≤ 1/20, mass ≤ 1/8. A run outside any of the three halts the study.

Three declared differences sit between the two mass figures, and this page measures none of their contributions: ESA reports re-entered mass while this catalogue sums dry mass; the two inclusion rules are not identical; and the reporting windows are defined separately. How much of the 30,661,491 g each carries is unmeasured, and attributing the spread to any of them is precisely what Act 1 is chartered to score.

Arm K — the TLS arm, because a client failure and an offline archive look identical. The host serving the merged nadir ozone record fails the TLS handshake against the system curl 8.7.1 / LibreSSL 3.3.6 on this platform with sslv3 alert handshake failure, exit 35, HTTP 000, while returning HTTP 200 and full content through a Homebrew curl built on OpenSSL (VERIFIED, measured this pass). The frozen ingest client is a curl linked against OpenSSL, with its exact version string recorded in every registry row at pull time; the system curl / LibreSSL stack is the refuting arm. An ingest run on stock system TLS reads a live archive as absent, and absence and refusal are different answers.

The halt conditions — instrument defects, distinct from losses

1. Two declared-identical rules executed twice on the same pinned bytes disagree on any row → broken scorer, halt.
2. The gram-exactness admission passes a value with four decimal places → halt.
3. The hydration arm fails to fire on 2022-01 → the adversary exclusion is broken and no physics is scored.
4. A response-archive query for a documented gap returns a verdict rather than GRANULE_ABSENT → halt.
5. Any of arm J's three spreads falls outside its frozen tolerance — events 1/20, payloads 1/20, mass 1/8, on the catalogue's own denominator → halt, re-pin, restart the seal.

The four recipe pieces, instantiated

The index states the rule: every charter must instantiate all four pieces, and "a study missing any one of them is not a shear study; it is a correlation hunt." All four are instantiated below. Pieces 1, 3 and 4 are executable today. Piece 2 is instantiated at archive level and its grading thresholds sit at corpus stage, which the piece itself states.

Piece 1 — a forcing with a computable clock and track

The catalogue, named exactly. Jonathan McDowell's GCAT General Catalog of Artificial Space Objects, a single anonymous tab-separated file at https://planet4589.org/space/gcat/tsv/cat/satcat.tsv. Measured 2026-08-31 (VERIFIED): HTTP 200, no login, no token, no user agent, 19,293,257 bytes, 42 columns, header banner line 2 reading # Updated 2026 Aug 30 2126:09.

Licence and release are attributed to the thing that carries them. The file itself contains exactly two non-data lines — the 42-column header and that banner — and no licence string and no release number anywhere in the bytes. The CC-BY-4.0 licence, the copyright note "This data may be freely reproduced as long as you cite it", the minimal citation form "Data from J. McDowell, planet4589.org" and the release number 1.8.7 (2026 Aug 25) are printed on the GCAT website, not in the file (VERIFIED as site text, and the distinction is stated because the digest below pins the file and not the site). Full attribution as the catalogue requires it: McDowell, J., General Catalog of Artificial Space Objects, https://planet4589.org/space/gcat. A charter may therefore pin, re-serve and republish the exact bytes it graded, which is what a frozen corpus requires. Columns used: Type, DDate, Status, DryMass, DryFlag, Inc, IF, Bus.

The corpus pin, with its digest. The catalogue is rewritten at the same URL as it updates, so a citation by URL alone does not identify the bytes a census was measured from. CC-BY-4.0 permits redistribution, so the graded bytes are re-served in the public research repository at corpus/study-29/satcat.tsv:

• 19,293,257 bytes
• banner line 2 # Updated 2026 Aug 30 2126:09
• sha256 090ce077eb05ef45fca04069b5d960e469c0242077c4ce9d1d1ee773e65f13df, recorded in corpus/study-29/SHA256SUMS and recomputable with shasum -a 256 corpus/study-29/satcat.tsv

Every census figure on this page is therefore replayable byte for byte, not merely in method, by any reader who pulls the corpus and runs the census program named in the reproduce section.

The clock. DDate — the catalogue's own definition, "the time when the object reentered the atmosphere" — read under its published Vague Date grammar, where precision is carried by how many tokens are present and a trailing ? widens the interval to about three times the stated precision. Precision is machine-readable per row from the string itself rather than assumed. Measured over the 2025 population (Status ∈ {R, AR, D}, n = 1,907): 501 rows year+month+day+HHMM with no uncertainty marker, 219 with HHMM and the marker, 1,162 day-only certain, 23 day-only uncertain, 2 year-only, 0 unclassed. The frozen epoch bin floor for the whole population is one day, with a sharper minute-resolved sub-census of 501 rows available as its own arm.

The track — and it is an inclination bound, not a ground point. A reentering object's ablation is confined to latitudes bounded by its orbital inclination. Frozen, in pure integers, with no propagator and no model: ic = Inc × 100 (exact Int64 centi-degrees), tc = ic > 9000 ? 18000 − ic : ic, and the row's ablation satisfies |φ| ≤ tc. Measured: Inc is present with exactly two decimals on 1,907 of 1,907 rows, and the companion quality flag IF is empty on 1,907 of 1,907 — zero flagged, zero absent. The latitude coordinate is exact on every row where the mass coordinate is absent on 654, which is why the track carries the confinement test.

The mass, exact in grams. A string-level regex census — never a float parse — of DryMass against ^-?[0-9]+$ and ^-?[0-9]+\.[0-9]{1,3}$ passes on 1,907 of 1,907 rows, 0 non-conforming. DryMass × 1000 is therefore an exact Int64 on every row: the lattice unit of the forcing ledger is the gram, and no rational, no rounding rule and no float enters the ledger anywhere.

The access ladder, measured, so the charter cannot overclaim. This catalogue is the only source probed that carries reentry epoch and dry mass and inclination in one anonymous file. Space-Track.org requires a free account — an anonymous decay query measured HTTP 401 while /documentation serves 200 — carries no mass field, and its TIP class is the only latitude/longitude corridor source found this pass; its documentation states verbatim that LAT/LON is "the location above which an object is predicted to arrive at 10km altitude during its descent, not the predicted Earth impact location" (VERIFIED), i.e. 50–76 km below the ablation altitude, a proxy that must be labelled as one. ESA's DISCOSweb — the upstream of every ESA mass figure — is closed to individuals by ESA's own eligibility text and was measured redirecting HTTP 302 to an OAuth endpoint at auth.sdo.esoc.esa.int. CelesTrak was unreachable from this host on two independent paths, which is a local reachability result and not evidence of an outage, and carries no mass column regardless — its RCS_SIZE is a three-valued radar-cross-section bucket. The charter therefore scopes its forcing to the anonymous epoch + mass + inclination-band ledger and states plainly that its track is a latitude band.

Piece 2 — a public raw response archive

The auth boundary, measured rather than assumed. Every directory index and every documentation PDF serves anonymously; every NASA granule is gated. A live pull of the newest limb-profiler aerosol file, OMPS-NPP_LP-L2-AER-DAILY_v2.5_2026m0830_2026m0831t134728.h5, returned HTTP 401 redirecting to urs.earthdata.nasa.gov/oauth/authorize (VERIFIED). The NASA CMR search API is fully anonymous, so pre-registration can be performed end to end on anonymous metadata and only ingest needs the free Earthdata Login, which the charter names as a stated precondition.

Lane	Product	Version / DOI	Geometry and cadence	Measured latency
A — aerosol extinction (primary)	OMPS_NPP_LP_L2_AER_DAILY	v2.5, DOI 10.5067/6X1B487WO4W1	HDF5 swath, one file/day; six independently retrieved wavelengths 510 / 600 / 675 / 745 / 869 / 997 nm; radiances normalised at tangent height 38.5 km; filter cuts extinction above 0.1 km⁻¹ and residual above 50%; the unfiltered field RetrievedExtCoeff_NOFILT is the graded arm; record start 2012-02-07. Vertical grid and altitude range not read from the product documentation this pass — owed at corpus stage.	1 day
A′ — continuity	OMPS_N21_LP_L2_AER_DAILY	v1.0, DOI 10.5067/FWE0H6HNGHFL	same instrument class on NOAA-21; record start 2022-11-10	—
B — profile ozone	OMPS_NPP_LP_L2_O3_DAILY	v2.6, DOI 10.5067/8MO7DEDYTBH7	HDF5, one file/day; 1 km geometric-altitude grid, 12.5 → 57.5 km; profile vertical resolution ~1.8 km	1 day
B′ — profile ozone	ML2O3 (Aura MLS)	v005, DOI 10.5067/Aura/MLS/DATA2516	HDF-EOS5, one file/day; ~165 km along-track profile spacing; −82° to +82°; useful range 261 → 0.001 hPa per the MLS v5.0x data quality document §3.18	2 days
B″ — hydration exclusion arm	ML2H2O (Aura MLS)	v005, DOI 10.5067/Aura/MLS/DATA2508	same cadence and geometry; useful range 316 → 0.001 hPa	2 days
C — solar occultation, reaching the injection band	g3bssp (SAGE III/ISS)	v6, DOI 10.5067/ISS/SAGEIII/SOLAR_HDF5_L2-V6.0	82,225 granules; 0.5 km grid to 100 km; aerosol extinction at nine channels, channel 1 at 384.12 nm; record start 2017-06-07	~1 month
D — total column	OMPS_NPP_NMTO3_L3_DAILY	v2, DOI 10.5067/7Y7KSA1QNQP8	exactly 1.0° × 1.0°, dimensions 360 × 180, first cell centre (−179.5, −89.5), explicitly non-synoptic	2 days
D′ — total column	OMTO3 / OMTO3d / OMTO3e	v004, DOIs 10.5067/Aura/OMI/DATA2424, /DATA3401, /DATA3402	L2 swath; 1.0° and 0.25° daily grids	2 days
D″ — merged nadir record	GSFC SBUV/OMPS Merged Ozone v8.7	anonymous ASCII	sbuv.v87.mod_v14.70-25.za.txt (168,056 B, 5° zonal monthly, 56 year blocks 1970–2025); sbuv_v87_mod.int_lyr.70-25.za.r3.txt (4,433,180 B, 21 pressure layers with boundaries stated in the file header)	monthly
E — composition	PALMS SABRE single-particle spectra	NOAA CSL, anonymous (directory HTTP 200, granule range request HTTP 206)	16 netCDF-4 files, 2023-02-21 → 2023-03-27; one file 78,557,928 bytes, 38,348 particles × 241 mass bins	closed campaign, no forward cadence

Two products are excluded by measurement, not by preference. The MEaSUREs merged product MSO3L3zm5 ends 2013-07-31 and cannot score a forward-registered event. OMPS_NPP_LP_L3_AER_MONTHLY v1.1 is gridded 5° latitude × 15° longitude, and the ledger's own band width is 5°, so the product's latitude cell equals the discriminating unit with zero margin — it cannot resolve the confinement claim, and only L2 daily products may be graded.

Raw means raw. Every lane above is L2 or L3 as served, including the limb profiler's unfiltered RetrievedExtCoeff_NOFILT arm, and never a figure lifted from a paper.

A discovery trap written into the charter. The DCOTSS aircraft collection's own metadata does not list PALMS among its instruments, yet 21 PALMS granules live inside it. The granule inventory is the instrument; the collection metadata is not. Those 21 granules are a different collection from lane E's 16 SABRE files, and whether they overlap, and whether either carries a forward cadence, was not established this pass and is owed. Neither is a drumbeat-scoring archive today, which is why the composition separator is excluded from the forward seal on cadence rather than on file count.

Crossing R — the read-once quantiser at the archive boundary

The forcing ledger is integer-native on the wire and earns its zero-float property by string census. The response archives are not: OMPS-LP extinction, MLS mixing ratios and SAGE III extinction are served as IEEE floats in HDF5 / HDF-EOS5. The house rule holds on both halves only if the crossing is declared, so it is declared here, at the site where it happens, once:

• Extinction, served in km⁻¹ → the graded integer is floor(value × 10⁹), unit 10⁻⁹ km⁻¹.
• Volume mixing ratio, served dimensionless → the graded integer is floor(value × 10¹²), unit parts per trillion, which is the substrate's own wire convention for a ratio (ratio_ppt, snr_ppt, closure_conc_ppt in the domain spine above).
• Both are performed once, at load, on the served array, with the scale factor frozen and the rounding rule floor, never round. No float re-enters after that step, and every threshold comparison, every concordance count and every seal is an integer comparison in the unit named.

This is the same many-to-one crossing the sensing edge is specified to perform in the instrument lane, stated in the same terms: an interval of served values maps to one lattice point, nothing downstream restores the interval, and the honest claim is exactness at the chosen resolution with the resolution published as a number a reader checks against the product's own reported precision.

The corpus stage on the response side, named because the thresholds are derived from it

The program's five-stage road is Charter → Corpus → Frozen law → Pre-registration → Public resolution, and the response-side thresholds belong at the second stage. They are not frozen here. Every phrase of the form "frozen per-level integer threshold" on this page means a threshold derived at corpus stage and frozen before the first pre-registered month.

The historical window from which they are derived, frozen here:

• OMPS_NPP_LP_L2_AER_DAILY v2.5 and OMPS_NPP_LP_L2_O3_DAILY v2.6, 2016-07-01 through 2019-06-30 — three complete years, beginning after the documented sparse window closes and ending before the first sealed adversary epoch.
• ML2O3 v005 and ML2H2O v005, the same window.
• g3bssp v6, 2017-07-01 through 2019-06-30 — two complete years, the record's own start being 2017-06-07.

The window deliberately precedes both sealed adversaries — the 2019/20 austral-summer smoke event and the January 2022 Hunga event — so that no threshold is derived from an interval containing an adversary it will later be asked to separate. What the corpus stage produces and freezes: the per-level integer anomaly threshold at each graded level, the graded level set, the minimum retrievals per band-month below which a band-month publishes UNSAMPLED rather than a score, the aerosol product's vertical grid, arm G's and arm G2's levels and thresholds, arm B's status class, arm B2's probe date, and arm I's row set with its per-rule admission check.

Piece 3 — a sealed adversary

SEAL: Hunga, 15 January 2022. It is sealed on four stated grounds, each of which is a property of the event rather than the outcome of a candidate survey: it perturbs both graded observables — stratospheric ozone and stratospheric aerosol; its published mechanism includes particle-surface chlorine activation, which is the mechanism proposed for alumina; its perturbation spans exactly the calendar years across which the reentry rate ramps; and no independent published index of it was found this pass that would let a grader regress it away. No enumeration of rejected candidates is published on this page, so this is the charter's stated selection basis and not a survey result. Size separation is forbidden by the program recipe, so the charter proposes three shape separators below and freezes LOSS (iii) for the case where none of them separates it.

Magnitude, attributed inline: 150 Tg of water raising the total stratospheric water burden by 10%, unprecedented in the observational record, with the perturbation's residence time quantified at about nine years, a burden nearly flat for two years and then declining at an e-folding time of about three years, returning to pre-event variability around 2030 (Zhou, Chen, Feng, Heddell, Dhomse, Mann, Pumphrey, Millán, Santee and Chipperfield, Communications Earth & Environment 7:198, 2026, doi:10.1038/s43247-026-03216-5 — REPORTED); 0.4–0.5 Tg SO₂, global-average stratospheric AOD 0.016 against a 0.010 excess over background, particle equivalent aerodynamic diameter 1.1 µm, the largest aerosol event since 1991 (Martinsson, Friberg and Sporre, Atmospheric Chemistry and Physics 25, 10677–10690, 2025, doi:10.5194/acp-25-10677-2025 — REPORTED); O₃ −14% and HCl −22% at Southern Hemisphere midlatitudes, ClO above +100% and HNO₃ +43% in the tropics, water distributed ~78% Southern Hemisphere / 22% Northern in 2022 (Wilmouth, Österström, Smith, Anderson and Salawitch, PNAS 120(46), e2301994120, 2023, doi:10.1073/pnas.2301994120 — REPORTED); source at 20.54°S 175.38°W with overshooting tops 50–55 km (Carr, Horvath, Wu and Friberg, Geophysical Research Letters 49, e2022GL098131, 2022, doi:10.1029/2022GL098131 — REPORTED). The nine-year residence time is why the adversary is sealed rather than assumed past: its decay tail overlaps the entire pre-registration window.

The three shape separators, none of them a size argument, and one of them not live.

1. Hydration. Reentry ablation of aluminium structures supplies no water. An Aura MLS ML2H2O anomaly is a positive exclusion flag, available at every level and latitude on a public L2 archive, one file per day. Live.
2. Impulse against drumbeat. Hunga is one epoch at one point. The reentry forcing is 97–250 catalogued events per month, every month, across many inclination bands. A frozen law requires the response to track the ledger's own month-by-month integer per-band mass vector. Whether a single-epoch injection can satisfy that requirement is scored in Act 2 rather than asserted here. Live.
3. Aerosol composition. Hunga's aerosol is sulfate formed from SO₂; the reentry hypothesis names alumina. Not live — the only lane that sees the metal is a closed campaign archive with no forward cadence, so this separator is excluded from the forward-registered separation.

The forward seal therefore rests on two live separators, not three.

SEAL AS SECOND ARM: the 2019/20 Australian New Year's fires. The sharper mechanism twin, because its published mechanism is aerosol-surface chlorine activation in the absence of polar-stratospheric-cloud temperatures — the same shape of claim made for alumina. Magnitude: 0.4 ± 0.2 Tg of smoke tripling stratospheric AOD in the southern extratropics, in a self-lofting smoke-charged vortex rising to 35 km (Khaykin, Legras, Bucci, Sellitto, Isaksen, Tencé, Bekki, Bourassa, Rieger, Zawada, Jumelet and Godin-Beekmann, Communications Earth & Environment 1, 22, 2020, doi:10.1038/s43247-020-00022-5 — REPORTED); ~1.0 Tg cumulative smoke mass with an e-folding decay of 19–20 months (Ohneiser, Ansmann, Kaifler, Chudnovsky, Barja, Knopf, Kaifler, Baars, Seifert, Villanueva, Jimenez, Radenz, Engelmann, Veselovskii and Zamorano, Atmospheric Chemistry and Physics 22, 7417–7442, 2022, doi:10.5194/acp-22-7417-2022 — REPORTED); HCl 50–60% below climatology with ClO and ClONO₂ enhancements peaking mid-2020, the same authors stating that this reactive-chlorine enhancement was an order of magnitude or more weaker than a typical winter polar vortex (Santee, Lambert, Manney, Livesey, Froidevaux, Neu, Schwartz, Millán, Werner, Read, Park, Fuller and Ward, Geophysical Research Letters 49, e2021GL096270, 2022, doi:10.1029/2021GL096270 — REPORTED); a modelled 3–5% reduction of southern mid-latitude total column ozone (Solomon, Stone, Yu, Murphy, Kinnison, Ravishankara and Wang, Nature 615(7951), 259–264, 2023, doi:10.1038/s41586-022-05683-0 — REPORTED).

Its separator is sign-valued and size-free. Absorbing organic carbon self-lofts, so its anomaly front ascends over weeks. Settling alumina would give a front that descends. Altitude tendency is available from the limb-profiler and solar-occultation archives and is the traveling-lag analog stated below; which direction each front actually takes is what Act 2 scores.

CARRY AS THE BACKGROUND ARM, not as the adversary: ordinary meteoric ablation. It is the physically identical process, which is precisely why separating on size is forbidden here. This page publishes no mass multiplier between the meteoric background and the reentry ledger, and the reason is the page's own subject: the two primary papers that publish such a ratio use different bases and differ by about 35× as a result (below). A multiplier without a declared base is exactly the failure this study is built to catch, so none is stated. What is carried instead are the verbatim figures with their own bases attached, and one exact rational separator: meteoric material clusters at an Al/Fe mass ratio of 0.015 ± 0.007 and Mg/Fe of 0.21 ± 0.1, and Murphy et al. (PNAS 120(43), e2313374120, 2023 — VERIFIED) state in the Figure 5 caption, scoped in that caption to all SABRE 2023 Alaska flights, n ≈ 175,000 particles: "Particles with an Al/Fe ratio of more than 0.1 have probable spacecraft influence and represent more than 20% of the particles with metals." Frozen exact rational separator: Al/Fe > 1/10, with niobium and hafnium as presence tests having no meteoric counterpart.

Why the background is carried as an arm and not sealed as an adversary: it does not announce individual events, so it cannot be pre-registered. That is charter reasoning about what pre-registration requires and not a sourced measurement of the background's shape — no seasonal, diurnal or latitudinal amplitude for the meteoric background was sourced this pass, and none is stated anywhere on this page.

Demoted to frozen pre-registered covariates, never sealed, by one stated rule. A confounder that publishes its own phase in advance is a covariate, not a look-alike; a sealed adversary must be something the shape test has to beat, not something an index hands you.

Covariate	Why it is not sealed	Frozen index
QBO	publishes its own phase in advance	equatorial zonal wind: the Naujokat / Free University of Berlin radiosonde series continued by KIT/IMK, mirrored in the NOAA ESRL/PSD monthly index series
11-year solar cycle	publishes its own phase in advance	F10.7 solar radio flux; Mg II core-to-wing ratio
ENSO	publishes its own phase in advance	Niño 3.4 SST index

No amplitude is printed for any of the three. The amplitudes in circulation for the QBO ozone signal and the solar-cycle band edges were reachable this pass only through search summaries, with the primary texts returning 403. The covariates are named with their archives and their amplitudes are owed.

Two primary papers publish reentry-against-meteoric aluminium ratios that differ by about 35×, and each states its own basis. Murphy et al. 2023 state verbatim: "The flux of aluminum from meteoroids is estimated to be 130 tons y⁻¹, of which about 20 tons y⁻¹ ablates. About 210 tons y⁻¹ of aluminum ablates from reentering spacecraft" — a ratio of 10.5× on their stated basis. Ferreira et al. 2024 state "The TOA aluminum injection from micrometeoroids is 141.1 metric tons/year" against 41.7 t from satellites in 2022 — a ratio of 0.30× on theirs. Murphy et al. state their comparison as ablated-to-ablated; Ferreira et al. state theirs as top-of-atmosphere to top-of-atmosphere. This page reports both bases and renders no verdict on either. The charter consequence is what this page does own: the ledger states, before scoring, whether it counts dry mass at reentry epoch or ablated mass, and no comparison to the meteoric background is meaningful until it does. That declaration is made in the frozen-integers section below.

Piece 4 — standing future events for pre-registration

The drumbeat, measured. Monthly event counts and exact gram totals of the Status ∈ {R, AR, D} reentry population, reproduced by the census program from the pinned corpus:

2025	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
events	250	233	193	223	202	113	98	97	122	146	111	117
grams	48,317,100	61,671,272	39,090,000	46,940,900	48,052,850	33,125,500	37,982,107	19,828,800	33,218,300	32,709,600	26,269,130	33,855,950

2026	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug (to the 30th, partial)
events	111	121	129	124	97	110	106	79
grams	33,989,255	41,294,097	35,604,300	61,442,155	23,464,850	40,062,100	26,165,700	16,000,200

That is the nineteen-month integer gram vector, published rather than owed. 2025-01 through 2026-07 is nineteen complete months; over those nineteen the count never falls below 97 (2025-08 and 2026-05) and the monthly mass never falls below 19,828,800 g (2025-08). The August 2026 column is partial at 79 events through the 30th and is excluded from both floors. The past floor bounds nothing forward. Each month's count and gram vector is registered as it lands.

Annual populations, both readings, for all four years. The catalogue carries rows whose DDate names a year and no month — year-only rows, and in some years quarter-precision rows — so a population total and a month-resolved total are different quantities and both are printed:

Year	Population {R, AR, D}	Population grams	Month-resolved rows	Month-resolved grams	Rows carrying no month
2022	2,470	253,240,238	2,468	253,232,238	2 rows / 8,000 g
2023	2,047	234,257,149	2,042	234,245,149	5 rows / 12,000 g
2024	2,197	429,840,482	2,196	429,838,482	1 row / 2,000 g
2025	1,907	461,213,509	1,905	461,061,509	2 rows / 152,000 g

The frozen 2025 population is 1,907 and the monthly census sums to 1,905 — the two EPOCH_YEAR_ONLY rows carry no month and 152,000 g, and they are published as absent from the monthly census rather than folded into a month. The same exclusion applies to all four years and is disclosed for all four, which it must be for a reader to compare one row against another.

The registry row carries the per-band vector, not the count, and the census program emits it for any single calendar month on request, from the same pinned bytes.

The forward manifest, anonymous and live. The Space Devs Launch Library 2, https://ll.thespacedevs.com/2.3.0/launches/upcoming/ — measured HTTP 200 with no key, count = 358 upcoming launches (VERIFIED). Per-launch fields verified present: net (T-0, ISO 8601 UTC), an explicit precision enum net_precision (first row {"id":2,"name":"Hour","abbrev":"HR","description":"The T-0 is accurate to the hour."}), window_start, window_end, status, last_updated, mission.orbit, rocket.configuration.full_name, and pad.latitude / pad.longitude. The decisive limit: there is no payload-mass field anywhere in the launch object — a recursive traversal of every nested key found mass only under pad.location.celestial_body.mass, which is the mass of Earth. Forward mass at risk is therefore not obtainable from this source; only forward event cadence and pad location are.

The pre-registration protocol, and its venue

The archives' own latencies constrain the ordering: the forcing ledger is updated daily and carries its own update banner, while the response granules run 1 day (limb profiler), 2 days (MLS, nadir L3) and about a month (solar occultation) behind, so the forcing ledger for a period is always available before the response granules for that period exist. Latency proves the registration could have preceded the granule pull; only a timestamped registry row proves it did, and that row is what the protocol requires. So the venue is named:

The venue is a registry page in this wiki, Study-29-Registry.md, following the pattern of the Study 06 registry and the Study 07 registry. That page does not exist yet. Creating it is a precondition on the first pre-registered month, and it is carried as an open issue.

One registry row carries, and nothing may be added to it after the response granule is requested: the calendar month M; the corpus sha256 of the satcat.tsv snapshot; the per-band integer gram vector L(M) under each declared rule carrying a complete frozen operator chain plus the study's own rule; the predicted confinement rank order; the predicted per-band ordering; the ingest client version string; and the row's own timestamp.

The frozen protocol, per calendar month M:

1. On day 1 of month M+1, pull satcat.tsv, record byte count and sha256, and freeze that snapshot as the month's corpus.
2. Compute month M's per-band integer species-mass gram vector L(M) = (g₀ … g₁₈) over the 19 frozen 5° turning-latitude band slots, under each declared rule carrying a complete frozen operator chain, plus the study's own declared rule. L(M) is post-yield species mass, not dry mass — the declaration and its consequence are stated in the frozen-integers section.
3. Write the registry row and publish it, before requesting any response granule for month M+1.
4. Then pull the response granules and score.

Standing supplementary registration: each forward launch is registered with its net, its net_precision token and its pad coordinates before the vehicle flies, so the ascent-alumina confounder is registered on its own clock rather than reconstructed afterward. The FAA Office of Commercial Space Transportation pages serve anonymously (/space/licenses HTTP 200, 115,054 bytes; /data_research/commercial_space_data HTTP 200, 98,141 bytes) but the data index is JavaScript-rendered and no dataset file URLs could be enumerated, so that lane requires hand-pinning before it may be a precondition, and is not claimed as available.

The two readings and where they disagree

Reading	What it holds constant	The observation that separates it	Sourcing
The continuum reading — the injected material and its consequence are fields on a grid; the verdict is the model's output in binary64	The magnitude: these models carry transport, radiation and, in most of them, chemistry, and nothing else in the field does	Published models disagree on the sign and on the dominant species. Whether that spread is attributable to declared admission rules and declared conversion coefficients is what Act 1's flip census scores; LOSS (i) is frozen for the case where it is not. Maloney et al. 2025 carry prognostic CARMA microphysics and radiation but, in the authors' own EGU abstract (EGU25-3866, doi:10.5194/egusphere-egu25-3866 — REPORTED), the work "does not consider important interactions between metallic reentry aerosol and stratospheric chemistry." Ryan, Marais, Balhatchet and Eastham (Earth's Future 10, e2021EF002612, 2022, doi:10.1029/2021EF002612 — REPORTED) and Barker et al. 2026 carry the chemistry but transport alumina as a bulk tracer with heterogeneous activation applied to a fixed 8% of emitted mass. Revell et al. 2025 carry both chemistry and prognostic microphysics; their alumina is launch alumina and they do not simulate reentry emissions. Vliex et al. 2026 attribute 87.7% of modelled depletion to NOx from reentry.	Model configurations VERIFIED where retrieved; two are UNKNOWN and named as such in Honest limits
The exact-integer ledger reading — the injected mass is a product of one count and a small set of exact rationals; the verdict is which side of an integer comparison a per-band vector falls	The shape: an integer comparison decided identically on every machine, from one anonymous file	(N objects admitted) × (dry mass in grams) × (ablated fraction, an exact rational per object class) × (aluminium fraction, an exact rational per object class) × (oxidation yield, an exact rational). Every term is a count or a ratio of integers; nothing in the product needs a continuum, a grid, a timestep, a reanalysis, or a floating-point operation.	Charter construction; every coefficient VERIFIED or marked from the paper that declares it
The null	Nothing. It predicts that every declared admission rule, executed on the identical frozen rows, ranks every month and every latitude band identically	This is what Section zero exists to test, and the study publishes LOSS (i) with the census totals and the zero if it holds. The null is retired only by the gate — arm A's replaced-coefficient control, the flip census, the shuffle null, the low-load bands and the zero-gram band — never by citation.	Design statement of this charter

The readings are to be separated on shape, never magnitude; separating on size is forbidden by the program recipe. The continuum reading is not the adversary because its numbers are the wrong size — for the transport and radiative questions it was built for, it is the only instrument there is. It is the object under trial because a countable quantity is being carried through it, and the counting half can be done exactly.

What the field itself has published about its own arithmetic, reported and not adjudicated. Barker, Marais and McDowell (Scientific Data 11:1079, 2024, doi:10.1038/s41597-024-03910-z — VERIFIED) tabulate their own ledger against four prior ledgers and attribute every difference to admission rules or conversion coefficients, verbatim: "Ryan et al. only included orbital, geolocated re-entries that in our database are ~64% of total re-entry mass"; "Schulz and Glassmeier only accounted for suborbital objects with a reported or inferred velocity ≥3.8 km s⁻¹, resulting in an annual mass influx of 0.89 Gg (28% of this study)"; "The Jain study estimated emissions by excluding suborbital objects, omitting nearly half (46%) of all re-entries, yielding only 0.04 Gg Al₂O₃ emissions in 2020 compared to our 0.59 Gg" — a factor of 14.75 on one year; and, on Ferreira et al. 2024, "We estimate more Al₂O₃ than Ferreira, as they convert 32% of re-entry Al to Al₂O₃, whereas we convert all Al to Al₂O₃." Ryan et al. 2022 state their own truncation verbatim: "We only include 185 geolocated objects in our simulation. If we were able to include NOx emissions from all 324 objects re-entering in 2019, stratospheric O₃ loss due to ablation, to first order, would be ~0.01%" — against a simulated 0.005%, a first-order linear correction that doubles the reported effect on an unchanged atmosphere. And Barker et al. 2024 record a coefficient difference against Ryan et al., verbatim: "our re-entry emission index for indirect thermal NOx is 40% compared to 100% in Ryan et al." Ryan et al. 2022 report the split as nitrogen oxides 51% / chlorine 49%; Barker et al. 2026 report ozone loss "dominated by chlorine from solid propellant." These are the field's own published statements about its own bookkeeping. This page reports them and renders no verdict on them; scoring them under one frozen ledger is the charter.

The exact-integer ledger

The reentry ledger, and the units artifact it dissolves

This subsection is measured arithmetic and is published as arithmetic. It is re-derived by reproduce/reentry-alumina-ledger.swift in exact Int64 rational arithmetic with no float anywhere, and it concerns only what is consistent between published figures. It concerns no atmosphere and it is not a finding about anyone's model.

Two Ferreira yield operators exist, both recovered from that paper's own print, and the page carries both rather than choosing silently.

• The headline operator, 3/25. Ferreira et al. 2024's 30 kg of Al₂O₃ per 250 kg satellite is 30/250 = 3/25 exactly. This is the operator the ledger below is frozen on, and it is the one the paper prints as its whole-satellite figure.
• The composed operator, 149/1250. The same paper's declared per-step coefficients compose to 3/10 × 8/25 × 149/120 = 149/1250, and 149/1250 × 250 kg = 149/5 kg = 29.8 kg — the paper's own printed sub-stoichiometric mass, with zero residue.
• They are not equal: 3/25 = 150/1250 against 149/1250, a difference of one part in 150 that comes from the paper printing ~30 kg where its coefficients give 29.8 kg. The exact rationals below hold under 3/25 and do not survive 149/1250, and both readings are printed so that no ratio on this page rests on an unstated rounding.

Maloney et al. 2025's own stated case, carried through the frozen 3/25 operator. More than 60,000 satellites on orbit at a five-year replacement life is 12,000 reentering per year. At the three representative bus masses, and at the circulating 2,400/yr reading of the same fleet:

Reading	Reentry mass per year	× 3/25 → alumina per year	× 149/1250 → alumina per year
12,000/yr at 260 kg	3,120 t	374.4 t (= 1872/5 exactly)	371.904 t
12,000/yr at 800 kg	9,600 t	1,152 t	1,144.32 t
12,000/yr at 1,250 kg	15,000 t	1,800 t	1,788 t
2,400/yr at 260 kg	624 t	74.88 t	74.3808 t

Both readings of the same fleet are printed because the published statement collapses two independent variables — count and bus mass — into one scalar. The 12,000/yr and 2,400/yr readings differ by exactly 5× at 260 kg, which is nothing but the count ratio 12,000/2,400. Quoting only the heaviest row of a program's own output is the defect this page exists to name, so no row is quoted alone.

And here is the artifact, scoped to the rows it is computed on. A 10 Gg/yr figure is reachable as reentry mass at the 800 kg row (9,600 t/yr) and is not reachable as alumina under the 3/25 operator at the 12,000/yr count on any of the three quoted bus masses: the largest alumina figure in the table is 1,800 t/yr, and reaching 10,000 t/yr would require a yield of 10,000/3,120 = 125/39 = 320.5% at 260 kg, 10,000/9,600 = 25/24 = 104.2% at 800 kg and 10,000/15,000 = 2/3 = 66.7% at 1,250 kg — the last is below unity but is 50/9 = 5.56× the frozen operator. The unreachability is a property of that count and those three bus masses, not a property of arithmetic: the same program's CHECK 4 prints the counterexample, 10,000 t/yr of alumina under 3/25 implying 83,333 t/yr of reentering mass and 320,512 satellites per year at 260 kg, against a stated case of more than 60,000 on orbit. So "10 Gg/yr" and "over 360 t/yr" are different quantities, and the ~28× that circulates between them is the arithmetic ratio of a mass figure to an alumina figure — 10,000/360 = 250/9 = 27.8×. That is a statement about two numbers and not an identification of what any circulating spread is caused by; whether Maloney et al. 2025 label 10 Gg/yr as reentry mass or as alumina is not confirmed from the source text and is carried as Open issue 3.

On one unit set the spread is small and exact, under the 3/25 operator. Comparing alumina to alumina at the 800 kg bus: 1,152 / 360 = 16/5 = 3.2× exactly. At the 260 kg bus the ledger derives 374.4 t/yr against Ferreira's stated "over 360 t/yr" — 374.4 / 360 = 26/25 exactly, so the ledger's figure stands 4.00% above 360 and Ferreira's 360 stands 14.4/374.4 = 1/26 = 3.85% below 374.4; both denominators are named because the two percentages are the same gap read from opposite ends. Two independently published figures, put on one unit set by an exact rational operator, land within 4% of each other, where a mass-against-alumina reading of the same two papers lands them 27.8× apart. Under the composed 149/1250 operator the same comparison gives 1,144.32 / 360 = 3.179 and 371.904 / 360 = 1.033 — neither an exact small rational, which is the whole reason both operators are printed.

The frozen integers

Every integer in this subsection was measured on the pinned corpus by the census program named in the reproduce section, or read verbatim from a named source, and none of them moves after scoring. What is not yet frozen: the per-level response anomaly thresholds and the graded level set (derived at corpus stage, window frozen above), the minimum retrievals per band-month, the aerosol product's vertical grid, arm B's status class, arm B2's probe date, arm G's pressure level and threshold, arm G2's level, threshold, unit and window, and arm I's row set with its per-rule admission check.

Ledger units and corpus.

• Mass unit: 1 gram. DryMass × 1000 is an exact Int64 on 1,907 of 1,907 2025 rows; the string-regex census gives 0 non-conforming.
• Latitude unit: 1 centi-degree. Inc × 100 exact on 1,907 of 1,907; the quality flag IF is empty on 1,907 of 1,907.
• Turning latitude: tc = ic > 9000 ? 18000 − ic : ic, integer, no transcendental. tc is bounded to [0, 9000] centi-degrees by that formula.
• Band width 500 centi-degrees; band index b = floor(tc / 500), so b ∈ {0 … 18} — nineteen band slots, eighteen full 5° bands plus the boundary bin at tc = 9000 (exactly 90°). The graded vector is L(M) = (g₀ … g₁₈).
• Corpus pin: corpus/study-29/satcat.tsv, 19,293,257 bytes, banner # Updated 2026 Aug 30 2126:09, sha256 090ce077eb05ef45fca04069b5d960e469c0242077c4ce9d1d1ee773e65f13df, CC-BY-4.0 per the catalogue's site terms.

The mass base, declared here because it decides whether Act 1 has content. L(M) is a per-band vector of post-yield species-mass grams under each rule, not of dry-mass grams. If L(M) were dry mass, then no admission-yield coefficient — not the thermal-NOx index, not the ablated fraction, not the molecule fork — could move any month's or band's rank order, LOSS (i) would be sealed by construction before the first row was read, and arm A could never fire. The study's own declared rule is the exception and is deliberately the identity operator on dry mass (below), which is what makes it the reference the others are compared against. And per the charter consequence of the 35× paragraph: the ledger counts dry mass at reentry epoch as its input quantity, and each rule's declared ablated fraction converts that to ablated mass inside that rule's own operator.

The 2025 population. Status {R, AR, D} = 1,907 rows, 461,213,509 g (R = 1,900 rows / 454,967,509 g; AR = 4 / 1,071,000; D = 3 / 5,175,000). Status {R, AR} = 1,904 rows, 456,038,509 g. Payloads (Type beginning P) = 1,124 rows, 272,922,509 g, which is 59.17% of the population mass. MASS_ABSENT = 654 rows. MASS_ESTIMATED = 864 rows, 349,108,250 g = 75.69% of the population mass; unflagged = 1,043 rows, 112,105,259 g. Whether active deorbits are admitted is itself a frozen admission decision, not a detail: Barker et al. 2024 admit them, Ferreira et al. 2024 scope to LEO payloads only.

The confinement bands, 2025, in grams. All nineteen slots, complete.

Band slot	Rows	Grams	% of 2025 mass
b=0 — [0°, 5°)	2	2,260,000	0.49
b=1 — [5°, 10°)	8	1,236,000	0.27
b=2 — [10°, 15°)	4	7,201,000	1.56
b=3 — [15°, 20°)	6	11,206,000	2.43
b=4 — [20°, 25°)	4	13,300,000	2.88
b=5 — [25°, 30°)	13	19,242,000	4.17
b=6 — [30°, 35°)	13	10,220,000	2.22
b=7 — [35°, 40°)	16	14,657,000	3.18
b=8 — [40°, 45°) — leading	110	74,230,100	16.09
b=9 — [45°, 50°) — low-load arm	10	2,614,000	0.57
b=10 — [50°, 55°) — leading	597	182,392,000	39.55
b=11 — [55°, 60°)	13	5,567,000	1.21
b=12 — [60°, 65°)	25	3,755,300	0.81
b=13 — [65°, 70°)	27	3,355,000	0.73
b=14 — [70°, 75°)	186	10,350,000	2.24
b=15 — [75°, 80°) — low-load arm	11	1,000,000	0.22
b=16 — [80°, 85°) — leading	748	97,522,109	21.14
b=17 — [85°, 90°)	114	1,106,000	0.24
b=18 — tc = 9000 exactly (90.00°) — zero-gram null arm	0	0	0.00
all nineteen slots	1,907	461,213,509	100.00

Table note, because a reader will add the column. Each percentage cell is rounded from that slot's own exact ratio, so the cells do not sum to a rounded total. The three leading slots carry 354,144,209 g of 461,213,509 g, which is 76.79% rounded from the exact ratio; adding the three rounded cells (39.55 + 21.14 + 16.09) gives 76.78. The exact ratio is the frozen quantity.

Slot separations among the three leading bands, measured: b=8 → b=10 has one intervening slot (b=9, the 0.57% low-load arm); b=10 → b=16 has five. The tightest separation the confinement test must resolve is therefore one 5° slot, which is the resolution constraint that excludes the 5°-latitude monthly L3 product.

Per-degree structure, measured at 1° resolution from the same pass, because a claim at 1° cannot rest on a 5° table. The three heaviest whole degrees of turning latitude are 53° (542 rows, 153,727,000 g, 33.33%), 82° (454 rows, 74,742,109 g, 16.21%) and 43° (80 rows, 44,097,000 g, 9.56%). The distribution has three modes and they sit inside the three leading 5° slots.

The modal object. Modal payload DryMass in 2025 = 248 kg on 448 objects (next: 290 kg × 81, 700 kg × 67, 275 kg × 60). By Bus, one constellation family accounts for 679 of 1,124 payload reentries (60.41%) and 211,684,000 g of 272,922,509 g (77.56%). Ferreira et al. 2024 build their yield on "a typical small satellite, representative of a mega-constellation node, with a total mass of 250 kg" — the measured mode of the real reentering payload population to within 2 kg. The ledger's exactness rests on the string-regex census passing on 1,907 of 1,907 rows and holds whatever the bus concentration is; the concentration figures are published because they say what the population is, not because the exactness depends on them.

The declared admission rules, enumerated

Six admission rules are named in the field's own comparison tables. One carries a complete frozen operator chain executable against this catalogue. Five do not, and are named without one rather than counted as if they did.

Rule	Admission set, as its own authors state it	Frozen exact operators on this page	Can it render L(M) today?
Barker, Marais and McDowell 2024	everything, with per-class rationals	ablation degree 3/10 core stages and fairings, 13/20 upper stages, 4/5 non-megaconstellation payloads and non-fairing components, 1 megaconstellation payloads and non-fairing components, 0 reusables; aluminium mass fraction 7/10 rocket-body core stages and fairings, 2/5 all payloads and components; oxidation yield 1; reentry NOx index 7/40 reusables, 2/5 discarded	Yes — ablated fraction × aluminium fraction × yield closes to a species mass on every admitted class
Ferreira et al. 2024	LEO payloads only	per-object: aluminium mass fraction 3/10; oxidised fraction of that aluminium 8/25; cluster mass per unit oxidised aluminium mass 149/120; survivability 1/20, so 19/20 ablates. Composed 149/1250; headline whole-satellite Al₂O₃ yield 3/25	No — the per-object operator is complete and reproducible from print, but the admission set "LEO payloads only" is not decidable from this catalogue's own fields this pass, and the population chain has fired LOSS (iv)
Maloney et al. 2025	as stated in the paper	oxidation yield 1 to Al₂O₃; oxygen-to-aluminium atom ratio 3/2	No — no aluminium mass fraction and no ablated fraction are given, so the chain does not reach a species mass from a dry mass
Ryan et al. 2022	orbital, geolocated reentries only — "~64% of total re-entry mass" in Barker's database	the indirect thermal-NOx index 1, frozen from Barker's verbatim comparison and the only operator this page carries for it	No — chain incomplete
Schulz & Glassmeier	suborbital objects at velocity ≥ 3.8 km s⁻¹ only — 0.89 Gg against Barker's 3.2 Gg	owed	No
Jain	suborbital objects excluded, omitting 46% of all reentries — 0.04 Gg against Barker's 0.59 Gg for 2020	owed	No

The study's own declared rule, stated in full because Act 1 scores against it. Admit Status ∈ {R, AR, D}, publishing the D subset separately as its own row. Admit every Type. Ledger unit: the gram of DryMass × 1000, exact Int64. Yield operator: the identity. Rows with DryMass = 0 print MASS_ABSENT and contribute to no sum; rows with DryFlag ? print MASS_ESTIMATED and are censused in both denominators. Band assignment by the dwell rule below. This rule is deliberately the null operator on dry mass: it is the reference each declared paper's rule is compared against, and it is the one rule for which a per-band rank order cannot move under any yield coefficient, by construction.

The census denominator, stated once and used everywhere on this page: two rules enter the flip census — Barker's, and the study's own identity rule — of which one is third-party. Arm A's mutated-Barker control is a third vector over the same rows and is a control, not a rule. Every other declared rule is named above with the step that is missing.

LOSS (iv) has already fired, on Ferreira et al. 2024. That paper's population chain does not close from print: 41.7 / 308.9 = 0.1350 and 5.36 / 121.8 = 0.0440, neither equal to the stated 0.30 nor to 0.30 × 0.95 = 0.285, and the two years scale by 7.78× on aluminium against 2.54× on reentered mass. That step prints UNREPRODUCIBLE_FROM_PRINT and is excluded from the flip census. The per-object yield operator and the population chain are different steps: 149/120 is recovered exactly from that paper's own printed 29.8 / 24.0 kg, and 149/1250 × 250 kg = 149/5 kg = 29.8 kg reproduces the printed figure with zero residue, so the yield operator is reproducible from print and remains published as the worked molecule fork. The population admission step is the excluded one. Ferreira re-enters when its Zenodo dataset (doi:10.5281/zenodo.10816830, not fetched this pass) closes the chain and its LEO-payload admission set is made decidable from catalogue fields.

The molecular fork, frozen as a rational with its source named. Al₂O₃ per 2 Al is the mass ratio 101.9600768 : 53.9630768 from the standard atomic weights Al 26.9815384 and O 15.999 as published by the IUPAC Commission on Isotopic Abundances and Atomic Weights (REPORTED — the commission's own table was not fetched this pass), both finite decimals and hence an exact rational, evaluating to 1.88944. The same 24.0 kg of oxidised aluminium yields 29.8 kg as Ferreira's sub-stoichiometric clusters and 45.35 kg as Al₂O₃ at an oxygen-to-aluminium atom ratio of 3/2 — a factor of 1.5217 on identical aluminium input (computed on the unrounded 45.3466 kg; a reader dividing the printed 45.35 by 29.8 lands on 1.5218, and the exact chain is the frozen one). Both accountings are admissible readings of the same 24.0 kg; which one a paper chose is a declared coefficient, and whether declared coefficients move rank orders is exactly what Act 1's flip census scores. Fully oxidising all 75 kg of a 250 kg object's aluminium to Al₂O₃ gives 141.7 kg = 56.68% of dry mass, against Ferreira's 29.8 kg = 11.92% — a 4.755× spread across two admissible accountings of one object.

The atom-count form, flagged rather than preferred. Ferreira et al. state that at steady state "436 aluminum atoms and 176 oxygen atoms constitute different AlO clusters, whereas Al clusters are comprised of 924 aluminum atoms", and those integers close against a bond-pair census (924 + 250 + 157 + 26 + 3 = 1,360 aluminium; 4 + 40 + 131 + 1 = 176 oxygen), giving the ratio 436 : 176 = 109 : 44 and an implied 1.23936 against the printed 1.24167 — a 0.19% spread. The publisher returned 403 to every method tried this pass and the quotation carries no figure, table or section pointer, so these integers are marked UNVERIFIED_FROM_PRINT and are not frozen as the preferred operator. The frozen operator is the printed 149/120, which is locatable in the paper's own printed masses.

The composition separator. Al/Fe > 1/10, exact rational, with meteoric calibration ratios Al/Fe 0.015 ± 0.007 and Mg/Fe 0.21 ± 0.1 (Murphy et al., PNAS 2023 — VERIFIED), carrying the SABRE-2023 Alaska scope stated at every point of use.

Response-archive integers, frozen with the products that carry them. Limb-profiler retrieval wavelengths 510, 600, 675, 745, 869, 997 nm; normalisation tangent height 38.5 km; filter cuts at extinction 0.1 km⁻¹ and residual 50%; ozone grid 1 km, 12.5–57.5 km. Solar-occultation grid 0.5 km to 100 km, 9 channels, channel 1 at 384.12 nm. Nadir L3 grid exactly 360 × 180 at 1.0°. MLS along-track spacing 1.5° great circle (~165 km), ~15 orbits/day, useful ranges 261–0.001 hPa for ozone and 316–0.001 hPa for water. Single-particle file 78,557,928 bytes, 38,348 particles × 241 mass bins. The aerosol product's own vertical grid is not among these and is owed at corpus stage.

The confinement analog

The response must live inside the turning-latitude band the ledger names, and the test is decided in integers with no model, no propagator and no float.

A satellite's sub-point latitude is bounded by its orbital inclination, so for a reentry row r the ablation is confined to |φ| ≤ tc(r), computed from the catalogue's own two-decimal field. This is the recipe's track in its honest form: not a ground point, but a latitude band with an exact integer bound. The forcing announces where it will deposit before the response archive is opened, and it does so in integers anyone can recompute from one anonymous file.

The band-assignment rule, reconciled with the bound it sits beside. The physical statement |φ| ≤ tc permits ablation anywhere from the equator to the turning latitude, while the ledger rule b = floor(tc / 500) places a row's entire mass in the single slot containing its turning latitude. These are different maps and the charter picks one and says why. The dwell law is the reason: for a circular orbit of inclination i, the fraction of ground track spent near latitude φ rises without bound as |φ| → i, so sub-point density is sharply peaked at the turning latitude and comparatively flat elsewhere. The frozen assignment is therefore turning-latitude assignment, b = floor(tc / 500), chosen on that argument and stated as a choice. The alternative — distributing a row's mass over slots 0 … b under a stated dwell weighting — is a different statistic and is named as the arm that would test the choice; it is not instantiated in v1 and is carried as an open issue.

The confinement statistic, frozen and float-free. For calendar month M the ledger emits the integer species-mass gram vector L(M) = (g₀ … g₁₈) over the nineteen band slots. The response archive emits, for the same month and the same slots, an integer vector A(M) = (a₀ … a₁₈) — a count of L2 profile retrievals whose quantised extinction, or quantised ozone mixing ratio, at the graded level set exceeds the per-level integer threshold, in the unit fixed by Crossing R. The criterion is a Kendall concordance computed as an exact integer:

• Over all band-slot pairs (i, j) with gᵢ ≠ gⱼ, count C concordant and D discordant.
• Tie rule on the response vector, frozen: a pair with aᵢ = aⱼ is neither concordant nor discordant, is excluded from C and D, and is counted and published separately as T_A. Response ties will be common when most slots carry no anomaly, and burying them in either bucket would decide the verdict by convention.
• Effective pair count, measured rather than bounded. The maximum over nineteen slots is C(19,2) = 171. On the 2025 annual vector all nineteen gram totals are pairwise distinct — eighteen populated slots with distinct totals plus the zero at b=18, which is distinct from all of them — so the annual vector admits the full 171. A single month admits fewer: 2025-08, the lightest month, admits 105. The count is computed per month from that month's own vector, never assumed.
• Admissibility floor, frozen: C + D ≥ 30. A month with fewer admissible pairs publishes INADMISSIBLE_SPARSE and is not scored.
• Threshold, frozen as an exact rational: n/d = 1/5. The criterion is the cross-multiplied integer comparison (C − D) × d ≥ n × (C + D), i.e. (C − D) × 5 ≥ 1 × (C + D). n = 1 and d = 5 do not move after scoring.

No correlation coefficient is constructed, no float is divided, and the whole statistic is a count of integer comparisons.

The resolution constraint that decides which product may be graded. The distribution is narrow and three-moded: three 5° slots carry 76.79% of the year's mass, the per-degree modes sit at 53°, 82° and 43°, and the tightest separation among the leading slots is one 5° slot. The monthly L3 aerosol product is gridded at 5° latitude — equal to the band width and to that separation, with zero margin — so it cannot resolve the confinement claim, and only the L2 daily products may be graded. The dwell argument above is why the mass sits at the turning latitude in the first place; the 5° figure is why a 5°-gridded product cannot see it.

The shape on which each sealed adversary is to be separated, and never the size.

• Hunga injected at a single point at 20.54°S and spread across 60°S–60°N, distributed ~78% / 22% between hemispheres in 2022. The frozen law requires a per-band vector concordant with the ledger's three-mode structure at the 1/5 threshold, and a single-point injection is scored against that requirement rather than against its magnitude. It also carries the hydration flag the reentry forcing does not. Whether either separator actually fires is what Act 2 scores; if neither does, LOSS (iii) prints.
• The Australian fires were a single austral-summer, single-hemisphere event rather than a monthly per-band vector, and their front direction is the sign-valued separator stated in the lag analog.
• Meteoric ablation is understood to be organised by the Earth's apex direction and season rather than by inclination shells — and that statement is charter reasoning, not a sourced measurement. No primary source for the meteoric latitudinal shape was retrieved this pass, and it is marked here rather than used as a discriminant.

The traveling-lag analog

The honest form of it is an ordering test, not an arrival-time test, and the reason is that the field's own published lag spans two orders of magnitude.

Ferreira et al. 2024 solve gravitational settling from a geometric altitude of 86 km and report verbatim that clusters take "up to 30 years to reach the altitude of 40 km", restating it as "these reentry byproducts may take up to 30 years to settle from the top of the mesosphere into the stratospheric ozone layer." Maloney et al. (EGU General Assembly 2025 abstract EGU25-3866 — REPORTED) give "months to two years" for accumulation in the polar regions from an injection between 60 and 70 km. Dhomse et al. 2013, as quoted by Schneider et al. (Atmospheric Chemistry and Physics 21, 989–1013, 2021, doi:10.5194/acp-21-989-2021 — REPORTED), put mesospheric nanoparticle residence at "about 4 years." Months, four years, thirty years — three published values for one quantity, from three different starting altitudes (60–70 km, 86 km, mesospheric) and three different particle treatments. No comparison of the three papers' particle-size assumptions is published here, and none is asserted as the cause of the spread. A pre-registered law cannot freeze a single lag from that range, and a window spanning the field's own extremes discriminates nothing. Therefore the absolute-arrival leg is not graded.

The frozen lag law — the sign and monotonicity of the anomaly front's altitude tendency. Define, on the graded archive's own vertical grid, the integer day index t_first(z) at which level z first exceeds its per-level integer threshold within the registered window.

• The frozen quantity is a physical extent, not a level count: 8 km of contiguous monotone front. On a 1 km grid that is K = 8 consecutive levels; on solar occultation's 0.5 km grid it is K = 16. Freezing the extent rather than the count keeps the criterion the same physical test on any served grid, including the aerosol product's, whose grid is owed.
• Criterion: t_first(z) non-decreasing as z decreases across that extent — a descending front.
• Scored on: g3bssp v6, 0.5 km grid, over 60–86 km — the PROMPT arm, and the only lane whose stated vertical range reaches the injection band.
• The Australian-fire arm is separated by the sign of exactly this quantity, because absorbing organic carbon self-lofts and its front ascends. The Hunga arm is not separated by lag at all — it is separated by the hydration exclusion arm.

The two altitude regimes, never pooled. Injection sits at 60–86 km — Maloney et al.'s "between 60 km and 70 km"; Ferreira et al.'s 86 km settling initial condition, with ablation modelled at 2,200 K over a 90 s worst case at an O₂ number density of 3.0 × 10¹⁹ m⁻³. The response of interest sits at 20–40 km — Ferreira et al. quoting that 90% of ozone is in the stratosphere with concentrations peaking 20–30 km, and taking 40 km as "the closest altitude of concern."

• PROMPT arm, at the injection altitude (60–86 km). Lag from reentry epoch is hours to days and the clock is computable at the ledger's own day-precision floor. Solar occultation is the only lane whose stated range reaches this band; the profile-ozone product's stated range tops out at 57.5 km, and the aerosol product's range is owed. Sampling adequacy is the whole question for an occultation instrument: the lane produces roughly 29 solar events per day globally, about 870 profiles per month, and the per-5°-band monthly profile count is not measured on this page and is owed. Frozen admissibility floor: 30 profiles per band-month. Below it the band-month publishes UNSAMPLED rather than a score, and a month in which fewer than three loaded slots clear the floor publishes the PROMPT arm as unsampled in full.
• DELAYED arm, at ozone-layer altitudes (20–40 km). No computable lag exists, and the multi-year integrated denominator it would be graded against is not defined on this page. The DELAYED arm is not instantiated in v1, and no scoring lane is frozen for it. When it is instantiated, the range it would use is 20–40 km on the profile-ozone product, and that is a statement of intent and not a frozen arm.

Because the discrimination cannot rest on lag, it rests on confinement. That is the structural consequence of the two-order-of-magnitude spread. Where Study 28's lag analog was a psychrometric root arriving instantaneously at a threshold, this one is a front whose direction is decidable and whose timing is not.

The field itself names the delay as structural. Ferreira et al. 2024, verbatim: "This suggests that concentrations of aluminum oxide compounds may start increasing in the mesosphere well before reaching the stratospheric ozone layer. This would introduce a noticeable delay between the beginning of the injection process when orbiting bodies are decommissioned and the eventual ozone-depletion consequences in the stratosphere." That is the traveling-lag analog with the field's own provenance, carried as the paper's statement and never restated as this page's verdict about any atmosphere.

What would close the gap: a published, size-resolved settling law with a stated uncertainty narrower than one decade, tied to a measured particle-size distribution rather than to a molecular-dynamics steady state. No such law was found in this pass, and this pass published no systematic literature search, so that is a search result and not a statement that none exists. Until one is pinned, the absolute-arrival leg stays frozen and ungraded — exactly as Study 28 froze its loss (ii) against an archive year that had not been published.

Act 1 and Act 2

Act 1 — the admission-rule flip census — is runnable today, anonymously, in integers, and nothing in it touches the sky. Each rule entering the census is re-executed on the frozen integer ledger, per calendar month, per band slot, against the study's own rule. A flip is sealed when two rules, on identical frozen rows, rank two months in opposite order by injected species mass, or place a row's mass in different slots, or produce opposite signs for a month-over-month change. A sealed flip row carries: the catalogue object id, DDate verbatim with its precision token, Status, Type, DryMass with its flag, Inc, the computed tc in centi-degrees, the two rule names, and the two integer gram results. It has not been run.

Act 2 — the confinement census against the response archives — needs the free Earthdata Login, the corpus-stage thresholds, and pre-registered forward months, and runs under the protocol and the registry row frozen in Piece 4. It has not been run.

The Eisenstein framing, and what survives verification

This section is framing rather than evidence: what is second-hand is labelled second-hand, what is measured is measured here, and what is an open question is not dressed as a claim.

The famous ranking is second-hand and is labelled so. The remark that there have been only three epoch-making mathematicians — Archimedes, Newton, Eisenstein is transmitted by Moritz Cantor, Allgemeine Deutsche Biographie vol. 5 (1877), pp. 774–775 (REPORTED), reporting a conversational remark; Cantor was taught by Gauss at Göttingen in 1849–51 but does not claim to have heard it himself, and it reached English through E. T. Bell, Men of Mathematics (1937) (REPORTED). Nothing in Gauss's own hand contains it. It is carried here as reportedly, transmitted by Cantor and is not load-bearing.

The firsthand record is better and carries the weight. Gauss's 1847 preface to Eisenstein's Mathematische Abhandlungen wins him "an honourable place beside his predecessors" (UNVERIFIED_FROM_PRINT — the preface itself was not fetched this pass) — and the predecessors Gauss names are Euler and Lagrange. Gauss to Encke, 23 June 1844: he could be of no help "by actual teaching, since he clearly has by far surpassed this stage." In 1845, proposing Dirichlet for the order pour le mérite, Gauss noted he had almost proposed Eisenstein instead. (Schappacher, Mathematics in Berlin, Birkhäuser 1998, pp. 55–60 — REPORTED.)

No source attaches a reason to any of it, and this page does not invent one. What Gauss actually studied is documented: of the fifteen Eisenstein papers in Crelle vol. 27 (1844), he read one in detail — the quadratic-reciprocity proof by multiple Gauss sums (Lemmermeyer, arXiv:2101.03344, p. 3 — REPORTED). And that proof is analytic: Weil observed it is virtually identical with Gauss's own sixth proof, the Gauss-sum proof (REPORTED). The admired object sits on the analytic side of any line one might try to draw.

Eisenstein worked on both sides. Eisenstein series are holomorphic modular forms on the upper half-plane — functions of a continuous variable whose only discreteness is the lattice they are summed over. He taught analysis in Berlin from 1847 and built an independent analytic theory of elliptic functions the same year. His reciprocity law is a stepping stone in Hilbert's Zahlbericht (1897), his lemniscate arithmetic is the source of the Shimura–Taniyama congruence relation, and Eisenstein series are the instrument by which Langlands constructed the continuous spectrum of automorphic forms.

The doctrinal anchor, and it is a discipline rather than a preference. Eisenstein's 1847 elliptic-function theory sums conditionally convergent series — series whose value depends on the order of summation — and he fixed the order. That is Eisenstein summation, it bears his name, and it is exactly the discipline a byte-exact substrate enforces: the delicacy is pushed out of the values and into an order the author fixes and holds. That is the connection this page claims.

Three statements about the lattice hold together, and none may crowd out the others.

One — the coordinate lattice. T⁸ = R⁸/Z⁸ is the coordinate quotient of the substrate's eight-axis wire tuple; its shipped extent is Study 30's subject and only the lattice question is treated here. The Eisenstein integers Z[ω] form a rank-2 lattice: hexagonal, isometric to A₂, determinant 3, kissing number 6. Z⁸ is cubic, determinant 1, kissing number 16. Even Z[ω]⁴ = A₂⁴ has determinant 81 and kissing number 24, so it is not isometric to Z⁸ — the determinants settle it before any finer invariant is needed.

Two — Z[ω] is a shipped, live law in this substrate, which is why the anchor is load-bearing rather than decorative. Two of the forty-eight served domains carry it as their new_law, quoted in full from the live catalogue at https://affine.earth/language-invariant/games:

domain	title	new_law
algebra	Rigidity / Eisenstein linking	L(w)=(q,r) in Z^2
dynamo	Stellar dynamo — integer (q,r) + rational n/d step	L(w)=(q,r)∈Z² + spin n/d ∈ Q, den>0; dipole→multipole is a Jordan swap, not float decay

Three — the eight-dimensional lattice that does carry an Eisenstein module structure is E8, and the substrate uses Z⁸. (Corrected 2026-09-18: read "the substrate uses Z⁸" as the TRANSPORT tier — the 42-byte frame of Z⁸ integer deltas frozen in Study 30's charter, no pod built. The COURT tier is admission by tetracode congruence, now counted in the E8 library entry: 240 minimal vectors at norm 3, index 9, ω-closure and the (1, 56, 126, 56, 1) spectrum. The Shannon framing that once refused E8 "for any particular signal" is retired there.) E8 is a free Z[ω]-module of rank 4 — concretely {x ∈ Z[ω]⁴ : x mod √(−3) lies in the ternary tetracode} — so multiplication by ω is an order-3 lattice automorphism, and the ω-commuting symmetry group is the complex reflection group 6·PSp₄(3), Shephard–Todd G₃₂, order 155,520 (Basak, arXiv:math/0508228, Journal of Algebra; Construction A over the Eisenstein integers, Conway & Sloane, SPLAG — REPORTED). By Viazovska (Annals of Mathematics 185 (2017) 991–1015, arXiv:1603.04246 — REPORTED) E8 is the densest sphere packing in R⁸ among all packings, periodic or not — not merely among lattices — at density π⁴/384; Fields Medal 2022. Its kissing number is 240, proven maximal in 1979 (Odlyzko–Sloane; independently Levenshtein — REPORTED).

Measured by this program, by direct integer enumeration (reproduce/z8-vs-e8-lattice.swift, re-run this pass):

lattice	kissing number	minimal norm	covolume
Z⁸	16	1	1
E8	240	2	1

Both lattices are unimodular, so at equal covolume the packing-density ratio is (√2)⁸ = 2⁴ = exactly 16. In the same dimension at the same covolume, E8 packs 16× denser and touches 15× as many neighbours.

E8's Eisenstein structure is real and not unique. E8 also carries Gaussian Z[i] and Hurwitz-quaternion structures, and is isomorphic to the icosian ring (Nebe lattice database; Baez, arXiv:1712.06436 — REPORTED). "E8 is Eisenstein" is true and singles out Eisenstein no more than it singles out Hurwitz. Choosing the Eisenstein structure is interpretation, legitimate because its unit group is precisely the six-fold hexagonal symmetry.

What the substrate actually uses, stated as behaviour. The shipped coordinate wrap performs a floored modulo per axis onto a fixed power-of-two span with the winding preserved — R⁸/(sZ)⁸, cubic, not E8. Whether to move the quantiser to E8 is an open question, not a claim and not a defect: it would change the quantiser, the spatial key, the wire format and every sealed digest, and none of those changes has been costed.

T⁸ is a flat torus. Every flat torus R^n/L is orientable and parallelizable for every L, because R^n/L is a compact abelian Lie group, so the adjective distinguishes nothing and is not used. The vQbit is conceptually like an irreducible element of Z[ω] — an irreducible element π is determined only up to its six associates {±π, ±ωπ, ±ω²π}, and that sixfold ambiguity is the hexagonal symmetry.

Where the instrument lane went

The A.E.P-1 pod, its four-tier validation gate, its hardware abstraction layer, its transport and energy arithmetic, its bill of materials and the shipped geometry of the wire tuple are not on this page. They are Study 30 — the sovereign edge pod, and the split is deliberate: an empirical hardware specification sitting inside this page dilutes the arithmetic it is meant to support. The one sentence that connects them: the same exactness argument that makes this reentry ledger gradeable in integers is what that pod is chartered to implement at the sensing edge — a wire specified to carry integer milli-units rather than floats, so that two nodes cannot quantise the same observation onto different lattice cells, which is the property behind Crossing R above and behind a ledger two graders replay from one digest-pinned anonymous file. No pod has been built and no tier has been scored, so what the pod does is a specification and what this ledger does is a measurement.

Honest limits

1. No single source carries epoch and mass and a ground corridor. The corridor exists only in Space-Track's TIP class, behind a free login, and its coordinate is the 10 km-altitude descent crossing — 50 to 76 km below the ablation altitude — which is a proxy and is labelled one. It does not close anonymously, and no anonymous source publishing a reentry latitude/longitude was found this pass.
2. The catalogue's inclination is the canonical operational orbit, not the osculating inclination at the reentry epoch. For a decaying low-Earth-orbit object it changes very little, so it is a good proxy — but it is a proxy. Closing it needs Space-Track gp_history at the last pre-decay epoch, login-gated and throttled at "less than 30 requests per 1 minute(s) and 300 requests per 1 hour(s)" with one GP query per hour.
3. 75.69% of the 2025 reentered dry mass carries the catalogue's own ? estimate flag (864 rows, 349,108,250 g). No uncertainty band for that flag is published on this page, because none was located in the catalogue's own documentation this pass; the flag is carried as a flag and both denominators are printed. Any mass threshold frozen against the full population inherits an unquantified band on three-quarters of its denominator, and no anonymous source that would quantify it was found this pass — DISCOS is the upstream of every ESA mass figure and is closed to individuals by ESA's own eligibility text.
4. Debris carries no mass in either catalogue — 654 of 1,907 rows read 0 — so the mass ledger is scoped to payloads and flagged rocket bodies, with the debris denominator published as absent rather than as zero. ESA states the identical structural rule for its own report, verbatim: "the debris and unidentified object types have no mass nor area indicated as part of this report."
5. The epoch clock is minute-resolved on only 501 certain rows of 1,907. The frozen bin floor for the whole population is one day.
6. The band-assignment rule is a stated choice, not a derivation. Turning-latitude assignment rests on the dwell argument given above; the distributed alternative is named and is not instantiated in v1.
7. The lag cannot be frozen, and this is the largest structural gap. Published settling times span months to about four years to thirty years, from three different injection altitudes and three different particle treatments. The traveling-lag analog is instantiated as an ordering test, the absolute-arrival leg is not graded, and the DELAYED arm is not instantiated in v1.
8. SAGE III per-band monthly sampling is not measured here. The global rate is about 29 solar events per day; the per-5°-band monthly profile count is owed, and the PROMPT arm publishes UNSAMPLED below the frozen floor of 30 rather than scoring a thin band.
9. The aerosol product's vertical grid and altitude range are not tabled, and the K = 8 front criterion is stated as a physical extent for that reason. Both are owed at corpus stage.
10. No public satellite product speciating aluminium or any metal in the stratosphere was found this pass. The limb profiler reports extinction at six wavelengths, solar occultation at nine plus size distribution; neither carries a chemical species field, and no metal-speciated satellite product was found in CMR under any keyword searched this pass. Composition is reached only by in-situ single-particle mass spectrometry, and that lane — though public and anonymous — is a closed campaign archive with no forward cadence, so the forward seal rests on two live separators rather than three.
11. Two PALMS granule counts sit on this page and are not reconciled. Lane E is 16 netCDF-4 files from the SABRE 2023 campaign; the DCOTSS collection separately holds 21 PALMS granules. Whether they overlap was not established this pass. Neither carries a forward cadence, which is the property the forward seal turns on, so the reconciliation is owed but does not move the seal.
12. Response granules require a free Earthdata Login. Directories, documentation PDFs and the entire CMR discovery API are anonymous, so pre-registration is fully anonymous and only ingest is gated.
13. The response-side grading thresholds are at corpus stage, not frozen here. The derivation window is frozen; the values are not.
14. The response archives serve IEEE floats and the ledger does not. Crossing R is the declared read-once quantiser that puts both halves on one integer lattice. Before that crossing the response side is float-served, and the zero-float property of this study holds from Crossing R onward on the response half and everywhere on the ledger half.
15. A TLS trap reads as archive absence. The merged-ozone host fails the system TLS stack on this platform and serves 200 through an OpenSSL-built client. The charter names the TLS stack and freezes the ingest client.
16. CelesTrak was unreachable from this host on two independent paths. That is a local reachability result, not evidence the service is down, and it carries no mass column regardless.
17. Barker et al. 2026's model configuration is UNKNOWN and is not asserted. The publisher, the preprint archive and the mirror all returned 403 or DNS failure to every method tried. The GEOS-Chem version, horizontal resolution, vertical level count, model top, meteorology driver, chemistry scheme and aerosol treatment were not retrieved. What stands is a property of the inventory — Barker et al. 2024 distribute it pre-gridded at 4°×5° and 2°×2.5° with 47 and 72 levels to 80 km — and not of the run. The citation is reduced to the verified DOI-only form.
18. Maloney et al. 2025's resolution and CARMA bin structure are UNKNOWN. Confirmed: WACCM6 coupled to CARMA sectional, 10 Gg/yr, 60–70 km injection. Not confirmed: horizontal resolution, level count, model top, bin count, tested size distributions. Model defaults are not asserted from general knowledge.
19. Whether Maloney et al. 2025 label 10 Gg/yr as mass or as alumina is not confirmed from the source. The units arithmetic above establishes consistency and makes no attribution.
20. Forward mass at risk is not obtainable. The forward manifest carries clock, precision, window, status and pad coordinates and no payload-mass field anywhere. The natural closing source — FCC IBFS filings — returned HTTP 403 from this host, and its field list, filing-search endpoint and whether dry mass is a required structured disclosure were never verified.
21. Ferreira et al. 2024's population chain does not close from print alone, LOSS (iv) has fired on it, and its LEO-payload admission set is not decidable from this catalogue's fields this pass. Its per-object yield operator is separately reproducible from print and is retained as such. Its primary text did not fetch this pass — the publisher returned 403 to every method tried — so every Ferreira figure on this page carries REPORTED or UNVERIFIED_FROM_PRINT and none carries VERIFIED.
22. The Ferreira atom-count integers are UNVERIFIED_FROM_PRINT. The quotation carries no figure, table or section pointer.
23. Five of the six named admission rules carry no complete operator chain executable against this catalogue — Ferreira (per-object operator complete, admission set not decidable, population chain excluded by LOSS (iv)), Maloney (no aluminium fraction, no ablated fraction), Ryan (one index only), Schulz & Glassmeier, and Jain. The census denominator is two rules — Barker and the study's own — and that number is used at every site on this page.
24. The solid-propellant ascent confounder has no frozen integer. It is the sharpest competing anthropogenic source — different clock (launch epoch), different altitude (direct stratospheric injection), different track (launch-site corridor), no descent lag. The generic 70/15/15 propellant composition is a secondary-source figure with no primary motor datasheet retrieved, and it must be pinned per motor before any integer is frozen against it.
25. No seasonal, diurnal or latitudinal amplitude for the meteoric background was sourced. No such amplitude is stated, no mass multiplier against the meteoric background is published, and the meteoric shape argument in the confinement section and the pre-registration argument in the background-arm section are both marked as charter reasoning.
26. The covariate amplitudes are not printed. The QBO ozone amplitudes and the solar-cycle band edges were reachable this pass only as search summaries with the primary texts returning 403, so the covariates are named with their index archives and their amplitudes are owed.
27. The substrate's own float gates are cited as passing and not as proof of absence. Measured this pass, 24 float-typed declarations live inside the paths the float ratchet scopes while the ratchet prints zero, because its pattern does not match the forms those declarations are written in and one of its scoped paths does not exist. The same standard this page applies to a published model's declared coefficients is applied to the instrument this page is written on.

Open issues

1. Create Study-29-Registry.md. It is the named pre-registration venue and it does not exist. It is a precondition on the first pre-registered month.
2. Derive and freeze the response-side integers at corpus stage over the frozen window: the per-level anomaly thresholds, the graded level set, the minimum retrievals per band-month, and the aerosol product's vertical grid.
3. Confirm against the source text whether Maloney et al. 2025's 10 Gg/yr is reentry mass or alumina. The units arithmetic is consistent either way and attributes nothing until this closes.
4. Name arm B's zero-count status class, arm B2's probe date, arm G's ML2H2O pressure level and threshold, arm G2's level, threshold, unit and window, and arm I's row set with its per-rule admission check. Each is pinned at corpus stage and each is currently owed.
5. Measure the SAGE III per-5°-band monthly profile count, or the PROMPT arm publishes as unsampled by default.
6. Re-test the Ferreira admission rule against its Zenodo dataset (doi:10.5281/zenodo.10816830) before it re-enters the flip census, make its LEO-payload admission set decidable from catalogue fields, and locate a figure/table pointer for the atom-count integers.
7. Freeze operators for Maloney, Ryan, Schulz & Glassmeier and Jain, or continue to publish the census denominator as two.
8. Reconcile the 16 SABRE files against the 21 DCOTSS PALMS granules, and give the composition lane a cadence or keep it out of the forward seal.
9. Pin the solid-propellant ascent confounder per motor from a primary datasheet before any integer is frozen against it.
10. Instantiate the distributed band-assignment arm as the test of the turning-latitude choice.
11. Quantify or retire the catalogue's ? estimate-flag band. No band is published today, and the limit that rests on it is stated without one.

What this study does not judge

• The atmosphere. The verdict this court is built to render is about which continuum a model chose and which of its own declared integers moved the answer. The page renders no claim of harm, no claim of ozone depletion, and no claim of ozone recovery. The sign is contested in the published literature and that contest is what is under test.
• Anyone's launch programme. Third-party figures are attributed inline with author, year and venue, tagged for provenance, and where the field is unsettled the page says so.
• Which published model is right. The page reports the field's own statements about its own bookkeeping and renders no verdict on them.
• Any built pod's performance. No pod exists; that lane is Study 30 and every hardware row there is a drawing.
• The physical state behind a quantised value. Crossing R is many-to-one. An integer carries the lattice cell, not the air.

Reproduce every number on this page

The corpus. Pull https://planet4589.org/space/gcat/tsv/cat/satcat.tsv (no credentials), or take the graded bytes directly from the public research repository github.com/gaiaftcl-sudo/uum8dSolarResearch at corpus/study-29/satcat.tsv. Verify with shasum -a 256 corpus/study-29/satcat.tsv, which must print 090ce077eb05ef45fca04069b5d960e469c0242077c4ce9d1d1ee773e65f13df against corpus/study-29/SHA256SUMS. The census below is replayable byte for byte from that digest.

The programs are self-contained Swift, no float in any law path, each printing the table it backs. Build and run with xcrun swiftc -O -swift-version 6 <file>.swift -o /tmp/out && /tmp/out.

File	Reproduces	Carries its own control arm
reproduce/reentry-alumina-ledger.swift	the entire ledger census, in one string-level pass — run as /tmp/out corpus/study-29/satcat.tsv <year> [month]: the population and per-status row counts and gram totals, the payload subset, MASS_ABSENT / MASS_ESTIMATED / unflagged with both denominators, the six epoch-precision classes, the complete nineteen-slot band vector with the three-leading exact subtotal and the measured slot separations, the per-degree modes, the monthly rows and grams for any year, the modal dry mass, the leading bus family, and the admissible band-slot pair count. The [month] argument emits the single month's per-band vector, which is what a registry row carries.	prints the gram-exactness admission fired in both directions: 1.234 admits at 1,234 g, while 1.2345, 12x and the empty string print MASS_NOT_GRAM_EXACT
reproduce/reentry-alumina-ledger.swift	the exact-rational reentry ledger: the 3/25 operator; the 12,000/yr count from Maloney's stated case; 3,120.0 t → 374.4 t, 9,600.0 t → 1,152.0 t and 15,000.0 t → 1,800.0 t; the 2,400/yr reading at 624.0 t → 74.88 t; and the printed comparison ratio = 3.20 x against Ferreira's 360 t/yr. The exact rational forms 16/5, 26/25, 125/39, 25/24, 50/9 and 250/9 are derived on this page and are not printed by the program — the program prints their decimal displays.	prints both unit sets side by side so the reader sees which quantity each published figure is
reproduce/z8-vs-e8-lattice.swift	Z⁸ kissing 16, E8 kissing 240, and the exactly-16 density ratio at equal covolume, by direct integer enumeration	the two lattices are each other's arm at equal covolume

All three programs are integer-only in every law path and carry no float operation, which is the condition for byte-identical output across hosts. Cross-host byte-identity is not measured here; the programs were run on one host.

The domain spine is re-derived from the live catalogue at https://affine.earth/language-invariant/games — 48 domain objects, 88 role objects, 54 capabilities, 13 games, 122 distinct may_ingest field names, no_float: true on 48 of 48, and a dead_equation / new_law pair on 48 of 48 — with one anonymous GET.

Cross-links

• Study 30 — The sovereign edge pod — the instrument lane this page split out: the four-tier validation gate, the shipped geometry, and the integer wire specified at the sensing edge.
• Study 28 — Wet-bulb threshold court — the direct precedent: an exact key against float instruments, a section-zero gate with control arms in both directions, losses published as losses, and a verdict about the instrument and never the physiology.
• Study 27 — Exact nuclear scattering — the sibling that replays a field's own published divergence in exact integers.
• Study 26 — Master regulator bonds — the status precedent for the response half: archives measured served, corpus not ingested, gate not run.
• Study 11 — Ehrhart volume shear — the arithmetic cousin: exact lattice counting against float evaluation of the same quantity, and the geometry domain's own new_law.
• Study 02 — Launch ionospheric holes — the other study whose forcing is a launch manifest with a published clock.
• Study 09 — Global convective bond — frozen integer thresholds on a terrestrial-sensing lane, where REFUSED is not clear sky.
• Study 06 registry and Study 07 registry — the registry-page pattern this study's pre-registration venue follows.
• Zero Float · Zero Shear — why the ledger is in grams and why Crossing R is declared at the archive boundary.
• Shear Studies Index — the program board and the four-piece recipe every charter must instantiate.

Status: OPEN — charter frozen 2026-08-31, corrected 2026-09-01. The board word is the weaker of a split state: the forcing half is at corpus stage with its integers frozen, the response half is at charter stage on the Study 26 / Study 27 precedent, and the index's own OPEN definition fits only the second. All four recipe pieces instantiated; Pieces 1, 3 and 4 executable today, Piece 2 executable at archive level with its grading thresholds at corpus stage over a frozen derivation window. The descriptive corpus census has been run and is published complete over all nineteen band slots, all twelve 2025 months, all eight complete 2026 months and four annual populations; no flip census and no confinement census has been scored, and no response granule has been requested. Forcing: GCAT satcat.tsv, anonymous CC-BY-4.0 per the catalogue's site terms, 19,293,257 B, banner 2026 Aug 30, sha256 090ce077eb05ef45fca04069b5d960e469c0242077c4ce9d1d1ee773e65f13df pinned in-repo and byte-for-byte replayable — 1,907 reentry rows in calendar 2025, dry mass exact in grams on 1,907/1,907 by string-regex census, inclination exact in centi-degrees on 1,907/1,907 with zero quality flags, 461,213,509 g total, 354,144,209 g of it (76.79%, rounded from the exact ratio) inside three of nineteen 5° turning-latitude band slots, with slot b=18 measured at zero rows and zero grams as the null arm. Measured ledger arithmetic, published as arithmetic under the frozen 3/25 operator, with the paper's composed 149/1250 operator printed beside it: Maloney's own stated case of >60,000 on orbit at a five-year life gives 12,000 reentries/yr — 3,120 t/yr at 260 kg → 374.4 t/yr alumina, 9,600 t/yr at 800 kg → 1,152 t/yr, 15,000 t/yr at 1,250 kg → 1,800 t/yr, and the circulating 2,400/yr reading → 74.88 t/yr, the two readings differing by exactly the 5× count ratio. 10 Gg/yr is reachable as reentry mass at the 800 kg row and is not reachable as alumina at that count on any of the three quoted bus masses; 10 Gg/yr and 'over 360 t/yr' are different quantities and 10,000/360 = 250/9 = 27.8× is the arithmetic ratio between them, attributed to no paper. Alumina against alumina is exactly 16/5 at 800 kg and exactly 26/25 at 260 kg under 3/25 — 374.4 stands 4.00% above 360 and 360 stands 3.85% below 374.4 — and neither ratio is exact under 149/1250. Archive: OMPS-LP L2 AER v2.5 and O₃ v2.6 (1-day latency), Aura MLS ML2O3/ML2H2O v005 (2-day), SAGE III g3bssp v6 to 100 km, PALMS single-particle spectra anonymous — directories and docs anonymous, granules behind a free Earthdata Login; Crossing R declares the read-once floor quantiser that carries served IEEE floats onto the integer lattice. Adversary sealed: Hunga 2022-01-15 with a ~9-year residence time, to be separated on hydration and drumbeat — the composition separator is a closed campaign archive with no forward cadence and is excluded from the forward seal, so two live separators carry it; second arm the 2019/20 Australian smoke, separated on ascending-against-descending front; meteoric ablation carried as the background arm with Al/Fe > 1/10 as its exact-rational separator and no mass multiplier published, because the two primary papers use different bases and differ by ~35×; QBO, solar cycle and ENSO demoted to frozen covariates with no amplitudes printed. Pre-registration: 97–250 catalogued events every month across nineteen complete months (2025-01 → 2026-07) with the full nineteen-month gram vector published, minimum 97 events and 19,828,800 g, and the past floor bounding nothing forward; forward manifest anonymous with per-row precision and no mass field; venue named as Study-29-Registry.md, which does not exist yet. Four losses each with a scored form, fourteen control arms (eleven tabled, plus G2, I, J and K) and five halt conditions frozen before scoring; confinement threshold frozen at n/d = 1/5 with a C + D ≥ 30 admissibility floor and a measured 171 admissible band pairs on the 2025 annual vector, 105 on its lightest month; LOSS (ii) frozen at the exact ratio 1/4; LOSS (iv) has already fired on Ferreira's population chain, so the flip census runs on two rules — Barker's and the study's own identity rule. The lag is an ordering test over 8 km of contiguous monotone front, the absolute-arrival leg is ungraded and the DELAYED arm is not instantiated in v1. Measured lattice: Z⁸ kissing 16 against E8 kissing 240 (corrected 2026-09-18: Z⁸ is the transport charter, E8 the court — see the E8 library entry), both unimodular, density ratio exactly 16 — and the substrate uses Z⁸, which is an open question and not a defect. The substrate's own float gates are cited as passing and not as proof of absence, with 24 float-typed declarations measured inside the paths the ratchet scopes while it prints zero. The instrument lane is Study 30. Verdict about the instrument, never the atmosphere.